No, your roommate is NOT allowed to go through your belongings and, if they take or discard any, you could sue them to recover the value of what is missing and/or report them to the police for theft. They must return your belongings to you if you want them (you have to pick them up; the roommate does not need to ship them).
The lockout you describe seems to be illegal--a landlord, let alone a roommate, cannot simply "kick out" someone. You may have legal grounds to be let back in and/or seek monetary compensation if interested.
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